Box and Whisker Graph Example

Introduction to box and whisker graph example:
A box and whisker graph is used to show a set of data so that you can simply see where most of the numbers are. Box plots are helpful in Quality Analysis for interpreting the division of data since it can easily show whether the data is distorted and if there are abnormal observations (outliers) in the dataset. Box plots are also very useful when huge numbers of observations are involved and when two or more datasets are being compared. The box and whisker plot  is a graphical representation of key values from abstract figures.

Methodology for Box and Whisker Plot:
In Box-and-whisker plot, the interior box represents the values from the lesser to higher quartile. The core line represents the median. The straight line extends from the minimum to the maximum value. Box plots show differences between datas without building any assumptions of the underlying statistical allocation. The spacing’s between the different parts of the box help indicate the degree of dispersion (spread) and skewness in the data, and identify outliers. Box plots can be drawn either parallel or perpendicularly. I have recently faced lot of problem while learning Median Statistics, But thank to online resources of math which helped me to learn myself easily on net.

Steps to Solve Box and Whisker Plot:

Step 1:The first step involves arranging the given data in an ascending order

Step 2:The second step involves find the median (Q1) for the entire data.

Step 3:After finding the median ,find the upper quartile and lower quartiles.

Step 4:Find the median for lower quartile (Q2) and upper quartile(Q3).

Step 5:Fiind the Minimum value and Maximum value.

Step 6:Plot these values for Q1,Q2,Q3 in the graph.

Step 7:Draw a box which joins all the median values.

Step 8:Draw a straight line from Minimum to maximum range.

Example:

Draw a  Box and whisker plot for the given data:

7,8,5,3,12,14,6,8,4,15,10

Step1: The first step involves arranging the given data in an ascending order

3,4,5,6,7,8,8,10,12,14,15

Step 2:The second step is to find the median (Q1) for the entire data.

Median Q1=8

Step 3:After finding the median ,find the upper quartile and lower quartiles

Lower quartile =3,4,5,6,7

Upper quartile = 8,10,12,14,15

Step 4:Find the median for lower quartile (Q2) and upper quartile(Q3).

Q1=5

Q­2=12

Step 5: Draw the graph and mark the positions of Q1,Q2 and Q3.

Step 6: Draw the box which joins Q1,Q2, and Q3.

Step 7: And draw the line which joins Minimum and Maximum value.